How does reinforcement learning with video data work?
In reinforcement learning, to learn off policy control, you need data on the states, actions and rewards at each time step. If, in addition to a recorded video, you had a recording of controller inputs, and could add reward data by hand, then you could use a standard reinforcement learning method, e.g. DQN. Simply run the DQN training loop as normal, but skip the parts where it acts in the environment, and only train on batches of recorded experience.

With only video data, your options are limited. However, it might still be useful, because a significant part of the challenge is a machine vision task. For a DQN agent, it will need to convert frames from the video (e.g. last 4 frames) into a prediction of the different rewards that it could get depending on which controller buttons are pressed. If you can teach a separate neural network to perform a vision task on relevant video data, it may may help. You could use the learned weights from the first layers of this network as the starting point for your Q values network, and it will likely speed up a DQN figuring out the relationship to its predictions. This sort of task switch following learning is called transfer learning, and is often used in computer vision tasks.

A possibly useful starting task if you have a video, but no controller or reward data, would be to predict the next frame(s) of the video, given say four starting frames (you need more than one so that the neural network can use velocity information). It should be possible to generate the training data using opencv or ffmpeg from your recordings.